The world's top 1,000 websites have been patched to protect their servers against the "Heartbleed" exploit, but up to 2% of the top million were still vulnerable as of last week, according to a California security firm.

On Thursday, Menifee, Calif.-based Sucuri Security scanned the top 1 million websites as ranked by Alexa Internet, a subsidiary of Amazon that collects Web traffic data.

Of the top 1,000 Alexa sites, all were either immune or had been patched with the newest OpenSSL libraries, confirmed Daniel Cid, Sucuri's chief technology officer, in a Sunday email.

Heartbleed, the nickname for the flaw in OpenSSL, an open-source cryptographic library that enables SSL (Secure Sockets Layer) or TLS (Transport Security Layer) encryption, was discovered independently by Neel Mehta, a Google security engineer, and researchers from security firm Codenomicon earlier this month.

The bug had been introduced in OpenSSL in late 2011.

Because of OpenSSL's widespread use by websites -- many relied on it to encrypt traffic between their servers and customers -- and the very stealthy nature of its exploit, security experts worried that cyber criminals either had, or could, capture usernames, passwords,\ and even encryption keys used by site servers.

The OpenSSL project issued a patch for the bug on April 7, setting off a rush to patch the software on servers and in some client operating systems.

The vast majority of vulnerable servers had been patched as of April 17, Sucuri said in a blog post that day.

While all of the top 1,000 sites ranked by Alexa were immune to the exploit by then, as Sucuri went down the list and scanned smaller sites, it found an increasing number still vulnerable. Of the top 10,000, 0.53% were vulnerable, as were 1.5% of the top 100,000 and 2% of the top 1 million.

Other scans found similar percentages of websites open to attack: On Friday, San Diego-based Websense said about 1.6% of the top 50,000 sites as ranked by Alexa remained vulnerable.

Since it's conceivable that some sites' encryption keys have been compromised, security experts urged website owners to obtain new SSL certificates and keys, and advised users to be wary of browsing to sites that had not done so.

Sucuri's scan did not examine sites to see whether they had been reissued new certificates, but Cid said that another swing through the Web, perhaps this week, would. "I bet the results will be much much worse on that one," Cid said.